Orbital Analysis for matched events on 20210813_010251.715_UK

Summary for Event
-----------------
shower ID 7 PER
Lg 61.62° Bg 37.87° Vg 59.32km/s
mass 0.08487g, abs. mag -2.1
Path Details
------------
start 1.55° 51.07° 110.19km
end   1.42° 51.01° 94.94km

Orbit Details
-------------
Semimajor axis 12.15A.U., eccentricity 0.92, inclination 114.39°, Period 42.33Y, LA Sun 140.23°, last Perihelion 2021-07-25

Full details below
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Input measurement type: Azimuth +east of due north for meas1, Elevation angle above the horizon for meas2

Uncertainties type:
 Purely geometric uncertainties

Reference JD: 2459439.543654116802
Time: 2021-08-13 01:02:51.715692 UTC


Plane intersections
-------------------
Intersection 1 - Stations: UK002K and UK002N
 Convergence angle = 32.01601 deg
 R.A. =  46.16784  Dec = +56.18113 deg

Best intersection: Stations UK002K and UK002N with Qconv = 32.02 deg


Least squares solution
----------------------
State vector (ECI, epoch of date):
 X =   3812587.75 +/- 162.41 m
 Y =  -1466399.87 +/- 134.56 m
 Z =   5024545.31 +/- 93.65 m
 Vx =    22592.11 +/- 844.02 m/s
 Vy =    23524.25 +/- 688.03 m/s
 Vz =    50772.79 +/- 1133.22 m/s

State vector covariance matrix (X, Y, Z, Vx, Vy, Vz):
+2.039604e+04, +1.615668e+04, +1.089581e+04, +1.011764e+05, +8.084362e+04, +4.161812e+04
+1.615668e+04, +1.352720e+04, +8.888617e+03, +8.131552e+04, +6.816641e+04, +3.313911e+04
+1.089581e+04, +8.888617e+03, +7.069045e+03, +5.656200e+04, +4.574408e+04, +2.438577e+04
+1.011764e+05, +8.131552e+04, +5.656200e+04, +5.811446e+05, +4.605134e+05, +2.578250e+05
+8.084362e+04, +6.816641e+04, +4.574408e+04, +4.605134e+05, +3.822742e+05, +2.002694e+05
+4.161812e+04, +3.313911e+04, +2.438577e+04, +2.578250e+05, +2.002694e+05, +1.222611e+05

Timing offsets (from input data):
    UK002K: -0.000258 s
    UK002N: 0.000000 s

Reference point on the trajectory:
  Time: 2021-08-13 01:02:51.715692 UTC
  Lon     = ++1.553655 +/- 0.0026 deg
  Lat     = +51.074524 +/- 0.0003 deg
  Lat geo = +50.889483 +/- 0.0003 deg
  Ht      =  110227.07 +/- 135.77 m

  JD dynamic   = 2459439.544454857707 
  LST apparent = 338.9622275778 deg
Radiant (apparent in ECI which includes Earth's rotation, epoch of date):
  R.A.      =  46.15795 +/- 0.3060 deg
  Dec       = +57.28378 +/- 0.6680 deg
  Azimuth   =  53.72417 +/- 1.0827 deg
  Elevation = +51.82854 +/- 0.1589 deg
  Vavg      =  59.78700 +/- 0.5217 km/s
  Vinit     =  60.34625 +/- 0.8893 km/s
Radiant (apparent ground-fixed, epoch of date):
  R.A.      =  46.35907 +/- 0.3060 deg
  Dec       = +57.06481 +/- 0.6680 deg
  Azimuth   =  53.99319 +/- 1.0827 deg
  Elevation = +51.64943 +/- 0.1589 deg
  Vavg      =  59.93596 +/- 0.5217 km/s
  Vinit     =  60.49521 +/- 0.8893 km/s
Radiant (geocentric, J2000):
  R.A.   =  46.33777 +/- 0.3260 deg
  Dec    = +57.08170 +/- 0.6687 deg
  Vg     =  59.31748 +/- 0.9046 km/s
  Vinf   =  60.34625 +/- 0.8893 km/s
  Zc     =  38.28119 +/- 0.1569 deg
  Zg     =  38.62312 +/- 0.1519 deg
Radiant (ecliptic geocentric, J2000):
  Lg     =  61.62357 +/- 0.4763 deg
  Bg     = +37.86585 +/- 0.5802 deg
  Vh     =  40.96407 +/- 0.5076 km/s
Radiant (ecliptic heliocentric, J2000):
  Lh     =  78.67054 +/- 2.0181 deg
  Bh     = +62.72745 +/- 1.1024 deg
  Vh_x   =  -3.68751 +/- 0.8568 km/s
  Vh_y   = -18.40494 +/- 0.7670 km/s
  Vh_z   = -36.41037 +/- 0.1317 km/s
Orbit:
  La Sun = 140.230417 +/- -0.0000 deg
  a      =  12.145363 +/- 112.2094 AU
  e      =   0.920717 +/- 0.0450
  i      = 114.385414 +/- 1.4201 deg
  peri   = 153.688477 +/- 1.5120 deg
  node   = 140.229962 +/- 0.0001 deg
  Pi     = 293.918439 +/- 1.5119 deg
  q      =   0.962919 +/- 0.0044 AU
  f      =  26.307745 +/- 1.5121 deg
  M      =   0.438551 +/- nan deg
  Q      =  23.327806 +/- 224.4190 AU
  n      =   0.023286 +/- 0.0178 deg/day
  T      =  42.326891 +/- 339934417.4332 years
  Last perihelion JD = 2459420.710913 (2021-07-25 05:03:42.851148) +/- 1.1600 days
  Tj     =  -0.063760 +/- 0.2781
Shower association:
  IAU No.  =    7
  IAU code =  PER

Orbit covariance matrix:
             e     ,     q (AU)   ,      Tp (JD) ,   node (rad) ,   peri (rad) ,    i (rad)
e   , +1.736950e-03, +1.630829e-04, +4.646793e-02, -6.643037e-08, +9.910354e-04, +9.097895e-04
q   , +1.630829e-04, +1.610324e-05, +4.509610e-03, -6.157286e-09, +9.685087e-05, +8.443592e-05
Tp  , +4.646793e-02, +4.509610e-03, +1.270548e+00, -1.758806e-06, +2.721912e-02, +2.411116e-02
node, -6.643037e-08, -6.157286e-09, -1.758806e-06, +2.676427e-12, -3.748678e-08, -3.660490e-08
peri, +9.910354e-04, +9.685087e-05, +2.721912e-02, -3.748678e-08, +5.837280e-04, +5.139407e-04
i   , +9.097895e-04, +8.443592e-05, +2.411116e-02, -3.660490e-08, +5.139407e-04, +5.007121e-04

Jacchia fit on lag = -|a1|*exp(|a2|*t):
 a1 = 0.000000
 a2 = 0.000000

Mean time residuals from time vs. length:
  Station with reference time: UK002N
  Avg. res. = 4.534e-06 s
  Stddev    = 2.13e-03 s

Begin point on the trajectory:
  Lon =     1.553344 +/- 0.0025 deg
  Lat =    51.074380 +/- 0.0003 deg
  Ht  = 110192.06 +/- 129.77 m
End point on the trajectory:
  Lon =     1.416218 +/- 0.0021 deg
  Lat =    51.011440 +/- 0.0003 deg
  Ht  = 94943.52 +/- 100.94 m

Stations
--------
        ID, Ignored, Lon +E (deg), Lat +N (deg),  Ht (m), Jacchia a1, Jacchia a2,  Beg Ht (m),  End Ht (m), +/- Obs ang (deg), +/- V (m), +/- H (m), Persp. angle (deg), Weight, FOV Beg, FOV End, Comment
    UK002K,   False,    -0.382860,    53.537770,   34.00,   0.000000,   0.000000,   106164.82,    96782.13,          0.008831,     43.85,     24.06,              79.39, 1.0000,    True,   False, {"ff_name": "FF_UK002K_20210813_010245_923_0430336.fits"}
    UK002N,   False,    -0.727590,    51.263100,   57.00,   0.177963,  21.253556,   110192.06,    94943.52,          0.009336,     14.92,     26.72,              34.90, 1.0000,    True,    True, {"ff_name": "FF_UK002N_20210813_010243_183_0442880.fits"}

Points
------
 No, Station ID,  Ignore,  Time (s),                   JD,     meas1,     meas2, Azim +E of due N (deg), Alt (deg), Azim line (deg), Alt line (deg), RA obs (deg), Dec obs (deg), RA line (deg), Dec line (deg),       X (m),       Y (m),       Z (m), Latitude (deg), Longitude (deg), Height (m),  Range (m), Length (m), State vect dist (m),  Lag (m), Vel (m/s), Vel prev avg (m/s), H res (m), V res (m), Ang res (asec), AppMag, AbsMag
  0,     UK002K,       0,  0.078292, 2459439.543655184098,   2.61661, -15.37578,              154.08044,  17.67176,       154.08491,       17.67505,      2.61661,     -15.37578,       2.61182,      -15.37375,  3810652.94, -1468414.51,  5020197.08,      51.057809,       +1.517144,  106164.82,  325159.58,       0.00,             5168.11,   297.95,      0.00,           57464.81,    -14.70,    -26.80,          19.39,  +1.47,  -1.09
  1,     UK002K,       0,  0.118468, 2459439.543655648828,   2.47266, -15.74397,              154.32417,  17.35432,       154.33871,       17.36503,      2.47266,     -15.74397,       2.45634,      -15.73735,  3809810.07, -1469292.16,  5018302.83,      51.050518,       +1.501232,  104395.62,  324814.34,    2251.41,             7419.53,   124.89,  56038.79,           57464.81,    -47.83,    -87.12,          63.11,  +1.07,  -1.49
  2,     UK002K,       0,  0.158608, 2459439.543656113558,   2.30513, -16.08295,              154.58131,  17.07053,       154.57979,       17.06940,      2.30513,     -16.08295,       2.30762,      -16.08365,  3809008.71, -1470126.58,  5016501.90,      51.043580,       +1.486093,  102713.84,  324500.10,    4391.92,             9560.04,  -156.90,  53326.07,           57464.81,      5.00,      9.12,           6.62,  +0.76,  -1.80
  3,     UK002K,       0,  0.198796, 2459439.543656578753,   2.12720, -16.50344,              154.86961,  16.71014,       154.87046,       16.71077,      2.12720,     -16.50344,       2.12711,      -16.50305,  3808039.78, -1471135.49,  5014324.35,      51.035184,       +1.467818,  100680.72,  324139.66,    6980.06,            12148.17,     6.05,  64400.76,           57464.81,     -2.78,     -5.07,           3.68,  +0.53,  -2.02
  4,     UK002K,       0,  0.238972, 2459439.543657043949,   1.96677, -16.89113,              155.13035,  16.37631,       155.13668,       16.38097,      1.96677,     -16.89113,       1.96043,      -16.88822,  3807151.52, -1472060.40,  5012328.09,      51.027480,       +1.451046,   98817.18,  323826.75,    9352.73,            14520.84,   -45.76,  59056.79,           58339.34,    -20.81,    -37.93,          27.56,  +0.45,  -2.10
  5,     UK002K,       0,  0.279148, 2459439.543657508679,   1.76817, -17.30642,              155.43366,  16.02466,       155.42682,       16.01963,      1.76817,     -17.30642,       1.77742,      -17.30957,  3806181.31, -1473070.64,  5010147.68,      51.019057,       +1.432738,   96782.13,  323505.02,   11944.26,            17112.37,   121.30,  64504.41,           59470.04,     22.47,     40.99,          29.80,  +0.31,  -2.24
  0,     UK002N,       0,  0.000000, 2459439.543654116802,  39.82134,  21.69993,               96.61184,  33.44198,        96.60815,       33.43857,     39.82134,     +21.69993,      39.82626,      +21.69946,  3812571.08, -1466417.23,  5024507.84,      51.074380,       +1.553344,  110192.06,  196125.02,       0.00,               44.53,  -100.99,      0.00,           60815.08,     13.73,      7.66,          16.53,  +2.56,  +1.10
  1,     UK002N,       0,  0.040360, 2459439.543654583860,  39.76501,  21.25370,               97.01496,  33.14478,        97.00722,       33.13768,     39.76501,     +21.25370,      39.77545,      +21.25272,  3811597.41, -1467431.07,  5022319.66,      51.065972,       +1.534998,  108147.61,  194014.08,    2600.78,             2645.31,    64.22,  64439.62,           60815.08,     28.44,     15.87,          34.62,  +1.91,  +0.47
  2,     UK002N,       0,  0.080696, 2459439.543655050918,  39.73927,  20.84504,               97.36050,  32.85564,        97.36833,       32.86279,     39.73927,     +20.84504,      39.72927,      +20.84602,  3810728.76, -1468335.56,  5020367.48,      51.058465,       +1.518608,  106323.98,  192140.02,    4921.06,             4965.59,   -49.63,  57523.64,           60815.08,    -28.45,    -15.86,          34.97,  +1.17,  -0.25
  3,     UK002N,       0,  0.121056, 2459439.543655517977,  39.67786,  20.40152,               97.76101,  32.56162,        97.76037,       32.56104,     39.67786,     +20.40152,      39.67920,      +20.40144,  3809798.36, -1469304.35,  5018276.52,      51.050417,       +1.501061,  104371.05,  190144.52,    7406.27,             7450.80,     0.01,  61576.09,           60815.08,      2.29,      1.28,           2.85,  +0.65,  -0.75
  4,     UK002N,       0,  0.161432, 2459439.543655985035,  39.63113,  19.94158,               98.15968,  32.24512,        98.16274,       32.24790,     39.63113,     +19.94158,      39.62778,      +19.94196,  3808856.87, -1470284.68,  5016160.65,      51.042265,       +1.483302,  102395.21,  188137.38,    9921.09,             9965.62,    78.29,  62285.18,           61075.71,    -10.90,     -6.08,          13.68,  +0.47,  -0.90
  5,     UK002N,       0,  0.201780, 2459439.543656452093,  39.55503,  19.50468,               98.56260,  31.96312,        98.54510,       31.94731,     39.55503,     +19.50468,      39.57877,      +19.50249,  3807974.63, -1471203.32,  5014177.94,      51.034619,       +1.466646,  100544.03,  186267.25,   12277.66,            12322.19,     0.01,  58406.02,           60768.83,     61.57,     34.40,          78.10,  +0.51,  -0.84
  6,     UK002N,       0,  0.242148, 2459439.543656919617,  39.53656,  19.06220,               98.91924,  31.64029,        98.92506,       31.64553,     39.53656,     +19.06220,      39.52997,      +19.06293,  3807109.50, -1472104.15,  5012233.66,      51.027115,       +1.450305,   98729.04,  184444.15,   14588.54,            14633.07,  -125.17,  57245.38,           60281.61,    -20.29,    -11.31,          25.98,  +0.33,  -1.00
  7,     UK002N,       0,  0.282548, 2459439.543657387141,  39.47609,  18.56908,               99.34745,  31.30405,        99.34868,       31.30516,     39.47609,     +18.56908,      39.47567,      +18.56924,  3806157.98, -1473094.93,  5010095.25,      51.018855,       +1.432346,   96733.18,  182452.93,   17130.16,            17174.69,   -21.54,  62911.41,           60298.00,     -4.26,     -2.37,           5.51,  +0.16,  -1.15
  8,     UK002N,       0,  0.322916, 2459439.543657854199,  39.43100,  18.11674,               99.72906,  30.98818,        99.73393,       30.99252,     39.43100,     +18.11674,      39.42604,      +18.11734,  3805304.62, -1473983.50,  5008177.43,      51.011440,       +1.416218,   94943.52,  180677.99,   19409.59,            19454.12,  -178.17,  56466.20,           60050.14,    -16.60,     -9.26,          21.70,  +0.57,  -0.71

Notes
-----
- Points that have not been taken into consideration when computing the trajectory have '1' in the 'Ignore' column.
- The time already has time offsets applied to it.
- 'meas1' and 'meas2' are given input points.
- X, Y, Z are ECI (Earth-Centered Inertial) positions of projected lines of sight on the radiant line.
- Zc is the observed zenith distance of the entry angle, while the Zg is the entry zenith distance corrected for Earth's gravity.
- Latitude (deg) and Longitude (deg) are in WGS84 coordinates, while Height (m) is in the EGM96 datum. There values are coordinates of each point on the radiant line.
- Jacchia (1955) deceleration equation fit was done on the lag.
- Right ascension and declination in the table are given in the epoch of date for the corresponding JD, per every point.
- 'RA and Dec obs' are the right ascension and declination calculated from the observed values, while the 'RA and Dec line' are coordinates of the lines of sight projected on the fitted radiant line. The coordinates are in the epoch of date, and NOT J2000!. 'Azim and alt line' are thus corresponding azimuthal coordinates.
- 'Vel prev avg' is the average velocity including all previous points up to the given point. For the first 4 points this velocity is computed as the average velocity of those 4 points.